This problem can be solved by setting up two equations to represent the number of enchilada and taco meals being served. Let x be the number of enchilada meals and y be the number of taco meals. Then we have:
x + y = 250 (representing the total number of meals)
5x + 7y = 1500 (representing the total cost of the food)
Solving these equations using methods such as substitution or elimination will give you the values of x and y, i.e. the number of enchilada and taco meals being served at the party.